Iterate an object along path
Select the curve, ALT C to convert from mesh to curve, Ctrl A to apply rotation and scale, in edit mode select the first point of the curve, Shift S "cursor to selected", then in object mode set "Origin to 3D cursor" (in the T panel).

Select the shape mesh, Ctrl A Apply rotation and scale, Origin to 3D cursor, add an array modifier and then a curve modifier, choosing the curve as target.

I had to smooth the curve where it bends nearly 90 degrees.